Here's how far I am in the "Win" camp over the "Play Well" camp:
When I saw this thread, I thought it was about whether it's more important for the team to actually win an individual game or perform well enough so that it SHOULD have won an individual game. i.e. is it better to get a win even though we played poorly through some luck or whatnot or to lose even though we played well. This to me is a legitimate argument because if you just got lucky, it means your team is not performing well and will likely lose future games.
What I can NOT get my head around is the idea that "playing well" means gorgeous, attacking football. I'm American and this mentality is just completely foreign to most Americans. In the most recent men's college basketball tournament (i.e. "March Madness") the team that won it all is the University of Virginia. While they had some offensive talent, their style of play was defense first. Many of their games were rather low scoring. And over the course of the whole season they won 35 games to 3 losses. None of their fans were saying "oh man, this low scoring, defensive style of basketball is soooo boring." They were loving the ride of being winners! American fans are completely supportive of getting the results however you have to get them, and if that means playing a grind-it-out style because your team can do that better than the other team, then grind it out and get those Ws, baby!
Just remember: winning isn't everything. It's the ONLY thing.